Why is (n-1)(n+1)=n^2-1?

11.06.2025 03:40

Why is (n-1)(n+1)=n^2-1?

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Move the nub up to the top:

Why are liberals so bad at grasping alternative facts? For example, if something doesn’t happen the exact same way Trump described it, liberals dismiss it as false; while conservatives are able to fully understand the underlying principle.

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The more direct answer is to look at a rectangle with sides of n + 1 and n - 1, let’s go with n = 2

n^2 - n + n - 1

Why are people so rude to debt collector’s? I am one and I am so tired of being mistreated. We are under paid and then have to deal with the most ungrateful, and disrespectful people. We aren’t customer service. Don’t get mad at us because YOU owe.

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If you cut off the end of that rectangle, you make it smaller, 2 * 3 and a separate nub of size 1 * 2

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(n - 1)(n + 1)

The basic answer is that you cross-multiply the values in each factor:

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And you are left with almost a square. One less than the square of side n.

n^2 - 1

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So, that’s a rectangle with sides 2 and 4.